MHB How Can You Test for Symmetry in Mathematics?

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To test for symmetry in mathematics, one can evaluate functions for symmetry about the x-axis, y-axis, and origin. The function y = 2x - 4 is analyzed, revealing it is not symmetric about the y-axis or the origin. When substituting -x into the function, the resulting expression does not match the original, confirming a lack of symmetry. The discussion emphasizes the importance of applying specific rules for testing symmetry in algebraic functions. Overall, understanding these symmetry tests is crucial for analyzing mathematical graphs.
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Test for symmetry about the x-axis, y-axis and origin.

| y | = 2x - 4

What are the rules for testing for symmetry?
 
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RTCNTC said:
Test for symmetry about the x-axis, y-axis and origin.

| y | = 2x - 4

What are the rules for testing for symmetry?

... have you researched "testing graphs for symmetry" ?

Algebra - Symmetry
 
Great! I will answer both symmetry questions tomorrow. Going to work now.
 
| y | = 2x - 4

| -y | = 2x - 4

y = 2x - 4

Symmetric about the x-axis?

| y | = 2(-x) - 4

| y | = -2x - 4

| y | = -2x - 4

Not symmetric about the y-axis.

| y | = 2x - 4

| -y | = 2(-x) - 4

y = -2x - 4

Not symmetric about the origin?
 

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I have been insisting to my statistics students that for probabilities, the rule is the number of significant figures is the number of digits past the leading zeros or leading nines. For example to give 4 significant figures for a probability: 0.000001234 and 0.99999991234 are the correct number of decimal places. That way the complementary probability can also be given to the same significant figures ( 0.999998766 and 0.00000008766 respectively). More generally if you have a value that...
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